Lynagh's family have requested that no details of his condition be disclosed by the hospital.
The 48-year-old, who won the World Cup with Australia in 1991, is reported to have suffered a stroke while visiting Brisbane.
Lynagh won 72 Test caps and retired from international rugby in 1995 as the world record points scorer with 911, a total which remains an Australian record.
An inspirational playmaker, Lynagh made his Test debut in 1984 and he was part of Australia's Grand Slam-winning team later that year.
Lynagh was vice-captain of Australia's World Cup-winning side in 1991 and he scored the late winning try against Ireland in the quarter-finals.
After captaining Australia to the quarter-finals of the 1995 World Cup, Lynagh retired from international rugby and joined Saracens at the start of the professional era.
Lynagh was the club's first major signing after Nigel Wray had taken control of the club and he helped attract Philippe Sella, Francois Pienaar and Kyran Bracken to the club.
Lynagh spent two years at Saracens, guiding them to a 48-18 victory over Wasps in the 1998 Tetley Bitter Cup final and he has been enrolled in the club's Hall of Fame.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.